Question

what is the slope of the line passing through (-2, 3) and (4, -5)?
-9
$-\frac{4}{3}$
-4
$-\frac{3}{4}$
question 16
1 pts
what is the slope of $5x - 3y = 6$?
$\frac{5}{3}$
$\frac{-5}{3}$
-3
5

Explanation:

Step1: Recall slope formula for two points

The slope $m$ between $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

Step2: Substitute (-2,3) and (4,-5)

$m=\frac{-5-3}{4-(-2)}=\frac{-8}{6}=-\frac{4}{3}$

Step3: Rewrite line to slope-intercept form

For $5x-3y=6$, solve for $y$:
$-3y = -5x + 6$
$y=\frac{5}{3}x - 2$
The slope is the coefficient of $x$.

Answer:

1. $-\frac{4}{3}$ (corresponding to the second option for the first question)
2. $\frac{5}{3}$ (corresponding to the first option for Question 16)